On the local cohomology of L-shaped integral FI-modules

Abstract

The local cohomology groups of FI-modules were computed in characteristic 0 by Sam and Snowden, but remain unknown integrally. In this paper we compute them for the Spechtral FI-modules corresponding to the L-shaped Young diagrams (i.e. the partitions (2,1,…,1)). We also find and discuss some interesting features of this computation, including the presence of torsion.